[Note: The ideas and opinions expressed in this work are
those of the author alone.]

The principle of equivalence was formulated by Einstein on the presumption
that from inside a closed compartment there is no way to tell whether the
compartment is accelerating in space or is stationary in a gravitational
field that would produce the same acceleration in the opposite direction
on a free falling mass in the compartment. Or, in terms of forces, that
a spring balance having a mass hanging on it would show the same stretch
if the compartment was accelerating upwards or if the compartment was stationary
on a planet with its gravity pulling it downwards.

Raising the presumption to the status of a postulate, Einstein concluded
that light traveling horizontally across the compartment would bend downward
under gravity since accelerating the compartment upward in space would cause
the light ray to do so. The flaw or error in the principle is right here
at the start.

The thought model used by Einstein uses a ray of light entering the compartment
from outside in a horizontal direction (perpendicular to the direction of
the gravitational force or to the direction of acceleration) through a tiny
hole in the wall of the compartment, say for example through the left wall,
(this is already equivalent to looking at outside from inside the compartment!)
and moves on to hit the right wall at some point on it. Since the compartment
is accelerating upwards and the speed of light though large is finite the
right wall would move upwards in that time to some extent. The path of light
would have been a straight line sloping downwards if the compartment had
been moving up at a constant speed. Since it is accelerating upwards the
speed keeps on increasing causing light to continually bend or slope down
more and more, relative to the inside of the compartment, until it hits
the right wall. So the path traced out would be a downward curve. Einstein
concluded light would trace out a similar curve under gravity with the compartment
stationary in it since he assumed impossibility of detecting the difference
between gravity and pure acceleration.

What Einstein failed to see was that the ray would bend downward not only
inside the compartment space as it was traveling across it but also at the
very point of entry in the left wall. Whatever the direction of a ray entering
through the hole in the wall was would keep on entering with greater and
greater downward slope and thereafter would bend further down through the
space in the compartment before hitting the right wall. The result would
be that the light spot on the right wall would not be stationary! The spot
formed on the wall would keep on moving downward and with increasing speed.
Whereas, under pure gravity with the compartment stationary in it the spot
formed on the wall would be stationary. The principle is in principle wrong!
We cannot have equivalence under the conditions. That is why a charged particle
sitting stationary inside the compartment would be able to sense pure acceleration
by radiating and sense pure gravity only by not radiating.

To save the situation we could try setting up the light source inside the
compartment fixed on the left wall so as to fire rays horizontally to the
right. In this way we also avoid the error of looking outside. Whatever
the upward speed of the compartment is the ray will come out horizontally
and travel to hit the right wall at a fixed point on it. Does this save
the situation? NO! It still does not produce the equivalence of gravity
and acceleration. Let us see why.

Consider the paths of a ray of light and of a Newtonian particle, which
we can call the test particle, both traveling horizontally at light speed c from left to the right across the compartment to hit the right
wall. Since both take the same time to reach the wall they both fall at
the same distance down from the horizontal level on the right wall if the
compartment is only accelerating upwards. Instead, if the compartment is
stationary and sitting on a planet and is subject to pure gravity only then
the paths are different. Light has mass due to its energy given by m = E/c2 (where m is the mass, E is its energy and c is
the speed of light) which makes E = pc, where p is its momentum by electromagnetic theory. For the test particle of equivalent
mass m energy E = ½pc = ½mc2.
Now gravity will cause both the masses to be attracted or pulled downward
and make their trajectories curve down. Since, to first order, the time
of flight across the compartment will be same, the downward change of momentum
will be the same for both light ray and test particle. The change in energies
for the two will however be different. The change of energy for the test
particle dE will be ½cdp while for the light ray
the change dE will be cdp, which is twice that for the
test particle. The change of energy is provided by gravitational force doing
work on either of them by displacing them down along the direction of force.
The only way light can gain twice the energy is by displacing twice the
vertical distance! Light will bend by twice the amount of a Newtonian particle.
Here we have already deduced the famous correct bending of light by gravity
without resorting to warping of space or usage of tensors representing curvatures
of space and time continuum. We simply recognized electromagnetic theory
as giving the correct dynamics of the light ray. Physicists had for lack
of insight used Newtonian dynamics for light in computing the bending of
light by the Sun and had gotten the wrong measure in spite of Maxwell having
laid down the correct formulae many decades before. When Einstein first
formulated his general relativistic formula for the bending using warping
of space it was not correct. Thanks to World War II his formula could not
be tested and found wrong and he had time to correct it. What did he correct?
I suspect (I do not know) he simply replaced E = ½mc2 by E = mc2 and as for all the tensor formulations
they were redundant for his equations become solvable only when space is
"flat" which is another way of saying curvatures of space are not there.
The curvatures are just a lot of confusion screening the simple truth: E = pc for pure energy. It is simply that transverse and longitudinal
inertias of moving bodies are not equal.

Now light is pure kinetic energy only. And we have seen that for its mass,
which we used for measure of gravitational force on it, it has half the
inertia of the equivalent test particle when forced transversely to its
direction of motion. Special Relativity gives the correct effect of this
reduced inertia of kinetic energy in a massive particle along directions
perpendicular to its motion. In Special Relativity we have both transverse
and longitudinal masses. The reduced inertia transverse to the motion of
a particle explain both the precession of perihelion of elliptic orbits
of planets and the collapsing of orbiting radius of binary neutron stars.
Since the transverse inertia of moving particles is reduced an elliptically
orbiting planet bends sharper than the Newtonian equivalent when near the
Sun as gravitational potential energy of the planet, which belongs to the
gravitational field, converts to kinetic energy of the planet as it nears
the Sun increasing its relativistic mass but with less than proportionate
increase of transverse inertia. This causes the pull of the Sun on it to
bend it towards the Sun more than by Newtonian amount (if we may call it
so) making it leave the Sun after going around it by tilting its orbit path
towards the Sun side.

In the case of binary stars orbiting each other in a circular manner there
is no precession but the bending around the common center is more than as
calculated by classical mechanics leading to falling in. It is simply reduced
transverse inertia causing the sharper bending. The more they bend in faster
they move due to loss of potential energy and faster they fall in. There
is no total energy change, hence, there is no ‘gravitational wave’ radiation
produced, potential energy keeps on changing to kinetic and the transverse
inertia keeps on decreasing relative to the increasing relativistic mass
and the rate of bending in keeps increasing to end up in collapse. There
is no such thing as gravitational waves.

Light cannot orbit around a mass under its gravity it simply collapses into
it since it curves sharper than a Newtonian particle and this gives the
correct conditions for black holes: using only Newton's gravity and E = pc.

What happens when light moves along the direction of a force that can act
on it, in this case along the direction of gravity? The equation is still
the same: dE = cdp. If we rewrite it as dp = dE/c we see that for a given change of momentum, whether
increasing or decreasing, light has to move twice the distance in the force
field compared to an equivalent Newtonian particle undergoing the same change
of momentum. For a Newtonian particle dp = 2dE/c.
For a massive particle this amounts to having a larger inertia, relativistically,
for a given mass than its corresponding Newtonian particle. This means that
a massive particle would accelerate or decelerate less than a corresponding
Newtonian particle under the force field. This can explain why the galactic
recessional deceleration decreases with increasing speeds! More the kinetic
energy greater is the mass but more than proportional is inertia greater.
Thus further the galaxies are from Earth slower they are decelerating due
to gravitational pullback. There is no need to invent the concept of ‘dark
energy’ to explain the decrease of deceleration of galaxies with distance
from Earth! It is all in the correct use of E = pc.

If we apply the idea to cosmic ‘big bang’ we have that in the beginning
there was light for 10-43 seconds in which time light expanded
space to Planck’s length and then there was creation of countless particles.
Expanding light would not decelerate but would lose energy at rapid rate
under the intense gravity of the huge mass of the light. The loss of kinetic
energy of light would become field energy. Such high energy in field results
in field particles. As light keeps expanding it keeps losing kinetic energy
creating field particles but what is happening is that later particles are
created after larger distances moved by light due to decreasing of gravity
and subject to lesser retardations being further from the gravitational
center of origin and, hence, are faster producing the velocity distribution
of particles that probably could explain Hubble's law of recession.

In retrospect we see that Einstein's theory of general relativity has masked
the equation E = pc in a cobweb of tensor analysis and
garbled a whole of a field of physics for ages. I understand that general
relativity makes even the so-called string theory almost untenable. The
truth is it has masked a simple equation of electromagnetism and done more
harm to physics than help it. Quantum theory of gravity, I believe, would
be possible if general theory of relativity were totally ignored. The fact
that stable bound system cannot be formed under gravitational forces, since
they collapse due to inequality of gravitational mass and inertial mass,
is probably the root cause of the problem. Gravitational and inertial masses
are equal only when the mass is at rest.